Equivalence Class

Tags

math

For an equivalence relation \( R \subseteq A \times A \) the equivalence class of \( a \in A \) with respect to \( R \) is the set of elements related to \( a \) by \( R \). \[ [a]_R = \{ x \in A : a R x \} \]

Set of Equivalence Classes

For an equivalence relation \( R \) the set of equivalence classes of \( A \) with respect to \( R \) is a partition of \( A \).